TITLE: Are there any limit questions which are easier to solve using methods other than l'Hopital's Rule?
QUESTION [19 upvotes]: Are there any limit questions which are easier to solve using methods other than l'Hopital's Rule? It seems like for every limit that results in an indeterminate form, you may as well use lHopital's Rule rather than any of the methods that are taught prior to the rule, such as factoring, rationalizing, trig limits, etc.
EDIT: These are great answers, thanks!

REPLY [3 votes]: If you want to evaluate
$$\lim_{x\to\infty}\frac{x^{1000000}+x^{999999}+\cdots+x+1}{x^{1000000}}$$
purely by use of L'Hopital's Rule, you will have to apply the rule a million times!